How can you write the expression with a ratio with a rationalized denominator 2+sqrt5/2-sqrt5

Just multiply 2-sqrt5 by 2+sqrt5 (this is what rationalising the denominator means), the same goes for 2+sqrt5:

(2+sqrt5) (2+sqrt5) / (2-sqrt5) (2+sqrt5)

(4+5) / (2-5)

9/-3

-3.